Subjective probability Explanation:

Here we will explain the subjective probability.

Numerical measure of the likelihood of an event to occur . If an observation which has n possible ways exhaustive and mutually exclusive and out of them in m ways in the event. A occurs, then the probability of occurrence of the event.

A is given by P(a = m/n.

If in a random sequence of n trials of an event, M are favorable to the event , the probability of that event occurring is the limit of the ratio M/n, when n is very very large , this lies between 0 and 1 .

P(a)=0 means that the event can not take place.

P(a)=1 means the event is bound to occur .

the events,A2,A3……..An are said to the mutually exclusive if ,

P(Ai ∩ Aj)=0 for i=1,2,3,……n.

J=1,2,3,…….n, I ≠ j

He events are said to be exhaustive if

P(A1)+ P(A2)+ P(A3)_………. P(An)=1 if ,

A ∩ B ≠ 0 then

P(A υ B)=P(A)+ P(B)

And if A ∩ B ≠ 0v then

P(A υ B)=P(A)+ P(B)-P(A B)

Subjective probability Example:

1. When you toss a coin , there are two ways it can fall. The subjective probability of getting a head on one roll of a coin is one chance out of two .

Solution:

P(h) means the probability of getting a head on one toss of a coin.

P(t) means the probability of getting a tail on one toss of a coin.

Step 1 : the number of favorable outcomes for head =1

Step 2 : the number of favorable outcomes for tail =1

Step 3 :number of possible outcomes =2

Step 4 : the probability of the event for head =number of favorable outcomes /number of possible outcomes